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Nonparametric Estimation of the Conditional Mode with Errors-In-Variables: Strong Consistency for Mixing Processes 

Authors: D. A. Ioannides a; E. Matzner-Loslashber b
Affiliations:   a Department of Economics, University of Macedonia, 54006 Thessaloniki, Greece.
b Laboratoire de Statistique, Universiteacute de Rennes II, 35043 Rennes, France.
DOI: 10.1080/10485250212375
Publication Frequency: 8 issues per year
Published in: journal Journal of Nonparametric Statistics, Volume 14, Issue 3 2002 , pages 341 - 352
Number of References: 13
Formats available: PDF (English)
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Abstract

Having two variables, an explanatory one ( X o ) and a response one ( Y o ), linked by the classical relation Y^lcuborcub = g(lcub\bf Xrcub^lcuborcub) + \varepsilon , we want to estimate the function g (.) without any parametric assumption. However, in a lot of situations, the variables are not measured directly but through their proxies lcub\bf Xrcub = lcub\bf Xrcub^lcuborcub + \bivarepsilon and Y = Y^lcuborcub + \eta where (o)macrand -are the measurements errors. We propose here a new method for estimating the function g (.) in such a context. Our estimator is based on deconvoluted kernels. Uniform convergence is established for strongly mixing stochastic processes. Some simulations show that our estimator is tractable and performs relatively well in practice.
Keywords: Deconvolution; Measurement Errors; Nonparametric Estimation; Conditional Density And Mode; Uniform Consistency; agr-mixing
view references (13) : view citations
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